- A kinetic model for vehicular traffic: Existence of stationary solutions (1998)
- In this paper the kinetic model for vehicular traffic developed in [3,4] is considered and theoretical results for the space homogeneous kinetic equation are presented. Existence and uniqueness results for the time dependent equation are stated. An investigation of the stationary equation leads to a boundary value problem for an ordinary differential equation. Existence of the solution and some properties are proved. A numerical investigation of the stationary equation is included.
- A Random Discrete Velocity Model and Approximation of the Boltzmann Equation (1992)
- An approximation procedure for the Boltzmann equation based on random choices of collision pairs from a fixed velocity set and on discrete velocity models is designed. In a suitable limit, the procedure is shown to converge to the time-discretized and spatially homogeneous Boltzmann equation.
- The Broadwell Model in a Box: Strong L1-Convergence to Equilibrium (1992)
- The global solution of the one-dimensional Broadwell model in the interval [1,0], with reflecting boundary conditions at 0, is shown to converge strongly in L1[0,1] to the constant equilibrium solution.
- Domain Decomposition: Linking Kinetic and Aerodynamic Descriptions (1993)
- We discuss how kinetic and aerodynamic descriptions of a gas can be matched at some prescribed boundary. The boundary (matching) conditions arise from requirement that the relevant moments (p,u,...) of the particle density function be continuous at the boundary, and from the requirement that the closure relation, by which the aerodynamic equations (holding on one side of the boundary) arise from the kinetic equation (holding on the other side), be satisfied at the boundary. We do a case study involving the Knudsen gas equation on one side and a system involving the Burgers equation on the other side in section 2, and a discussion for the coupling of the full Boltzmann equation with the compressible Navier-Stokes equations in section 3.